Question

Prove or disprove that there exists a constant $K$ such that $|f(x)-f(y)|\leq K |x-y|,\;\;\forall\;\;x,y\in[0,1]$

score 195 · Answer 1 · 2026-04-15 17:06:43

195

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Prove or disprove that there exists a constant $K$ such that $|f(x)-f(y)|\leq K |x-y|,\;\;\forall\;\;x,y\in[0,1]$

Published on 15 Apr 2026 - 17:06

score 61 · Answer 2 · 2026-05-04 11:07:58

61

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Limit of difference versus limit of quotient

Published on 04 May 2026 - 11:07

score 78 · Answer 3 · 2026-04-21 16:22:24

78

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If $a_{n+1}\leq (1-\alpha_n)a_n+\alpha_n\beta_n,\;\;n=1,2,3,\cdots$, then prove that $a_n\to 0$ as $n\to\infty.$

Published on 21 Apr 2026 - 16:22

score 116 · Answer 4 · 2026-04-15 19:50:08

116

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If $\rho_{n+1}\leq\rho_{n} +\sigma_n,\;\;\forall\;\;n\geq N_0,$ then prove that $\lim\rho_n=0.$

Published on 15 Apr 2026 - 19:50

score 64 · Answer 5 · 2026-04-11 22:12:30

64

Views

How to Prove or disapprove the following proposition?

Published on 11 Apr 2026 - 22:12

score 68 · Answer 6 · 2026-04-24 18:07:56

68

Views

Prove limit of sequence at infinity

Published on 24 Apr 2026 - 18:07

score 48 · Answer 7 · 2026-04-13 00:59:17

48

Views

Determinate $\lambda\in R$ so that the following equation has 2 real,distinct solutions.

Published on 13 Apr 2026 - 0:59

score 194 · Answer 8 · 2026-04-17 06:20:12

194

Views

Evaluate $\lim_{n\to\infty}\frac {qn+1}{qn} \frac {qn+p+1}{qn+p} \cdots \frac {qn+np+1}{qn+np}$ where $p\in\mathbb{N}\setminus\{0,1\},q>0.$

Published on 17 Apr 2026 - 6:20

score 71 · Answer 9 · 2026-04-11 05:02:12

71

Views

What does the l equals to?

Published on 11 Apr 2026 - 5:02

score 389 · Answer 10 · 2026-04-12 16:29:21

389

Views

Determining if a limit of a infinite series exists

Published on 12 Apr 2026 - 16:29

score 245 · Answer 11 · 2026-04-24 18:03:59

245

Views

Evaluating limits with fractions

Published on 24 Apr 2026 - 18:03

score 87 · Answer 12 · 2026-04-21 12:44:37

87

Views

Does the derivative of $f(x)=\begin{cases}\dfrac{x}{2}+x^2\sin\left(\dfrac{1}{x}\right)& x\neq 0,\\0, &x=0\end{cases}$ exist everywhere?

Published on 21 Apr 2026 - 12:44

score 93 · Answer 13 · 2026-04-15 16:08:01

93

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Evaluating a limit $\lim_{x\to 0}\left\{\dfrac 2{x^3}(\tan x- \sin x )\right\}^{2/x^2 }$

Published on 15 Apr 2026 - 16:08

score 57 · Answer 14 · 2026-04-17 05:44:42

57

Views

Test $x_1=0, x_{n+1}=\frac{9+(x_n)^2}{6}$ for convergence and find its limit.

Published on 17 Apr 2026 - 5:44

score 65 · Answer 15 · 2026-04-25 08:38:14

65

Views

Evaluating $\lim_{(x,y)\to(0,0)}(x^2+y^2)^{x^2y^2}$

Published on 25 Apr 2026 - 8:38

List Question

Prove or disprove that there exists a constant $K$ such that $|f(x)-f(y)|\leq K |x-y|,\;\;\forall\;\;x,y\in[0,1]$

Limit of difference versus limit of quotient

If $a_{n+1}\leq (1-\alpha_n)a_n+\alpha_n\beta_n,\;\;n=1,2,3,\cdots$, then prove that $a_n\to 0$ as $n\to\infty.$

If $\rho_{n+1}\leq\rho_{n} +\sigma_n,\;\;\forall\;\;n\geq N_0,$ then prove that $\lim\rho_n=0.$

How to Prove or disapprove the following proposition?

Prove limit of sequence at infinity

Determinate $\lambda\in R$ so that the following equation has 2 real,distinct solutions.

Evaluate $\lim_{n\to\infty}\frac {qn+1}{qn} \frac {qn+p+1}{qn+p} \cdots \frac {qn+np+1}{qn+np}$ where $p\in\mathbb{N}\setminus\{0,1\},q>0.$

What does the l equals to?

Determining if a limit of a infinite series exists

Evaluating limits with fractions

Does the derivative of $f(x)=\begin{cases}\dfrac{x}{2}+x^2\sin\left(\dfrac{1}{x}\right)& x\neq 0,\\0, &x=0\end{cases}$ exist everywhere?

Evaluating a limit $\lim_{x\to 0}\left\{\dfrac 2{x^3}(\tan x- \sin x )\right\}^{2/x^2 }$

Test $x_1=0, x_{n+1}=\frac{9+(x_n)^2}{6}$ for convergence and find its limit.

Evaluating $\lim_{(x,y)\to(0,0)}(x^2+y^2)^{x^2y^2}$

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